← openxiv:gr-qc.2026.00003 · gr-qc
The predictive content of Spectral Causal Theory
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We catalog the predictions of Spectral Causal Theory (SCT) — the one-loop gravitational effective field theory derived from the Chamseddine–Connes spectral action S = Tr f(D²/Λ²) on an almost-commutative spectral triple encoding the Standard Model — and classify them by their dependence on the cutoff function f. Cutoff-independent sector (determined by the Seeley–DeWitt a₄ coefficient and the SM multiplicities; rational arithmetic formally verified in Lean 4): • α_C = 13/120 (Weyl² coefficient) • c₁/c₂ = −1/3 at conformal coupling ξ = 1/6, frozen under matter-only one-loop RG flow • α_R(ξ = 1/6) = 0, excluding Starobinsky inflation in the standard spectral action • Gravitational wave speed c_T = c (Euclidean derivation, paper 4) • Absence of a scalar gravitational mode at ξ = 1/6 • Logarithmic black hole entropy correction c_log = 37/24 (conditional on stated assumptions) Black hole sector: modal stability of Schwarzschild QNMs is proven analytically via V > 3f/r² > 0 for ℓ ≥ 2; one-loop frequency shifts are bounded by δω/ω ~ c₂(ω/Λ)² ~ 10⁻²⁰ for stellar masses, fifteen orders below current LIGO sensitivity. Tidal Love numbers k₂ ≠ 0 (qualitatively distinct from the vacuum-GR k₂ = 0 result), but unmeasurably small at any plausible Λ. The paper builds on results from six companion papers: form factors for all SM spins (paper 1, 274 checks), solar system and laboratory bounds yielding Λ > 3.53 meV (paper 2, 332 checks), the a₈ chirality theorem ensuring one-loop UV finiteness unconditionally (paper 3), the nonlinear field equations and FLRW reduction (paper 4), the no-scalaron decoupling (paper 5), and the parameter-free CJ bridge formula C₀ N^{8/9} E² T⁴ verified to N = 15,000 (paper 7). A quantitative comparison with five competing programs (LQG, asymptotic safety, CDT, perturbative string theory, infinite-derivative gravity) across nine axes — covariant gravitational waves, BH entropy log correction, Lorentz invariance, primordial GWs, dimensional reduction, scalar mode, Love numbers, vacuum stability, and UV completion — identifies three discriminating observables (logarithmic entropy coefficient measurement, vacuum stability tests near μ ~ Λ, tidal Love number bounds in extreme-mass-ratio inspirals) and five explicit falsification criteria. Each result is labeled proven / verified (to 100-digit precision) / established / conditional, with assumptions stated explicitly.
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